In many common signal transmission environments, multiple signal sources are active at the same time. (For instance, in the real world, many acoustic sources in the environment may be simultaneously generating sounds.) A receiver (such as a listener) often would like to attend to a single signal source, but any sensor (e.g. microphone) in the environment typically responds to a mixture of sources. As indicated schematically in FIG. 1, each component of such a sensor's response corresponds to some source, delayed by the propagation time between that source and the sensor, and further filtered by echoes, radiation characteristics of the sources, and so forth. We call such a component a sensor image of its source.
It has been considered useful to be able to recover the underlying source signals from the available response mixtures, so that a listener could listen to each signal source separately. This is the source separation problem.
In a very important and common version of the source separation problem, the radiated signals of the underlying sources are not observable in any way. That is to say, they cannot be detected, measured, or recorded in isolation. Rather, the only available relevant information is the response signals generated by the sensors (e.g. microphones) that are present in the environment. The signals from those sensors (the “response mixtures,” “sensor mixtures,” or simply “mixtures”) can be detected, captured, and processed.
From a signal processing perspective, the situation may be modeled as shown in FIG. 2. In this model it is assumed that the observable signals m are composed of convolutive mixtures of the unknown sources s. The relationship between the hidden source signals and the observable mixtures are defined by a hidden “mixing matrix” H. An important signal processing challenge is to estimate those underlying but hidden sources by processing the observed sensor responses to create Source Images. This is referred to as the Blind Source Separation (BSS) problem.
A distinct and separate problem is to determine the component sensor images of each source. Note that, in general, none of the sensor images of a source will be identical to the corresponding hidden source signal. Nor will one of the sensor images of a source be identical to another image of the same source. Instead, each sensor image constitutes an independent view of its source. Because there are many signal processing systems that either require or can take advantage of multiple independent images of a signal source, particularly if each image can be associated with a specific sensor, it would be particularly advantageous to decompose every sensor signal into its constituent sensor images.